Design Optimization in Nonlinear Mixed Effects Models Using Cost Functions: Application to a Joint Model of Infliximab and Methotrexate Pharmacokinetics

PFIM 4.0, an extended R program for design evaluation and optimization in nonlinear mixed-effect models

BACKGROUND AND OBJECTIVE

Nonlinear mixed-effect models (NLMEMs) are increasingly used for the analysis of longitudinal studies during drug development. When designing these studies, the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. The function PFIM is the first tool for design evaluation and optimization that has been developed in R. In this article, we present an extended version, PFIM 4.0, which includes several new features.

METHODS

Compared with version 3.0, PFIM 4.0 includes a more complete pharmacokinetic/pharmacodynamic library of models and accommodates models including additional random effects for inter-occasion variability as well as discrete covariates. A new input method has been added to specify user-defined models through an R function. Optimization can be performed assuming some fixed parameters or some fixed sampling times. New outputs have been added regarding the FIM such as eigenvalues, conditional numbers, and the option of saving the matrix obtained after evaluation or optimization. Previously obtained results, which are summarized in a FIM, can be taken into account in evaluation or optimization of one-group protocols. This feature enables the use of PFIM for adaptive designs. The Bayesian individual FIM has been implemented, taking into account a priori distribution of random effects. Designs for maximum a posteriori Bayesian estimation of individual parameters can now be evaluated or optimized and the predicted shrinkage is also reported. It is also possible to visualize the graphs of the model and the sensitivity functions without performing evaluation or optimization.

RESULTS

The usefulness of these approaches and the simplicity of use of PFIM 4.0 are illustrated by two examples: (i) an example of designing a population pharmacokinetic study accounting for previous results, which highlights the advantage of adaptive designs; (ii) an example of Bayesian individual design optimization for a pharmacodynamic study, showing that the Bayesian individual FIM can be a useful tool in therapeutic drug monitoring, allowing efficient prediction of estimation precision and shrinkage for individual parameters.

CONCLUSION

PFIM 4.0 is a useful tool for design evaluation and optimization of longitudinal studies in pharmacometrics and is freely available at http://www.pfim.biostat.fr.

Design evaluation and optimization for models of hepatitis C viral dynamics

Mathematical modeling of hepatitis C viral (HCV) kinetics is widely used for understanding viral pathogenesis and predicting treatment outcome. The standard model is based on a system of five non-linear ordinary differential equations (ODE) that describe both viral kinetics and changes in drug concentration after treatment initiation. In such complex models parameter estimation is challenging and requires frequent sampling measurements on each individual. By borrowing information between study subjects, non-linear mixed effect models can deal with sparser sampling from each individual. However, the search for optimal designs in this context has been limited by the numerical difficulty of evaluating the Fisher information matrix (FIM). Using the software PFIM, we show that a linearization of the statistical model avoids most of the computational burden, while providing a good approximation to the FIM. We then compare the precision of the parameters that can be expected using five study designs from the literature. We illustrate the usefulness of rationalizing data sampling by showing that, for a given level of precision, optimal design could reduce the total number of measurements by up 50 per cent. Our approach can be used by a statistician or a clinician aiming at designing an HCV viral kinetics study.

Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0

Nonlinear mixed effect models (NLMEM) with multiple responses are increasingly used in pharmacometrics, one of the main examples being the joint analysis of the pharmacokinetics (PK) and pharmacodynamics (PD) of a drug. Efficient tools for design evaluation and optimisation in NLMEM are necessary. The R functions PFIM 1.2 and PFIMOPT 1.0 were proposed for these purposes, but accommodate only single response models. The methodology used is based on the Fisher information matrix, developed using a linearisation of the model. In this paper, we present an extended version, PFIM 3.0, dedicated to both design evaluation and optimisation for multiple response models, using a similar method as for single response models. In addition to handling multiple response models, several features have been integrated into PFIM 3.0 for model specification and optimisation. The extension includes a library of classical analytical pharmacokinetics models and allows the user to describe more complex models using differential equations. Regarding the optimisation algorithm, an alternative to the Simplex algorithm has been implemented, the Fedorov-Wynn algorithm to optimise more practical D-optimal design. Indeed, this algorithm optimises design among a set of sampling times specified by the user. This R function is freely available at http://www.pfim.biostat.fr. The efficiency of this approach and the simplicity of use of PFIM 3.0 are illustrated with a real example of the joint PKPD analysis of warfarin, an oral anticoagulant, with a model defined by ordinary differential equations.